Invasion and non-invasion on a time-periodic domain

TL;DR

This paper investigates conditions under which one species can invade or be blocked from invading another in a reaction-diffusion system on a domain that moves or varies periodically, extending previous results to more general and periodic settings.

Contribution

It extends invasion criteria to time-periodic domains and more general reaction terms, broadening the understanding of species invasion dynamics.

Findings

Identifies conditions for species invasion in periodic domains

Provides criteria for non-invasion scenarios

Extends previous invasion results to more general reaction systems

Abstract

For a two-species reaction-diffusion-competition system on a domain that translates at constant speed and/or whose boundary varies periodically with time, we prove sufficient conditions such that one species can, and cannot, invade an established population of the other. These results extend those of Potapov and Lewis (2004) to the periodic case, and to more general reaction terms.